Surface sensitivity is an important factor that determines the minimum amount of biomolecules detected by surface plasmon resonance (SPR) sensors. We propose the use of oblique-angle-induced Fano resonances caused by two-mode coupling or three-mode coupling between the localized SPR mode and long-range surface plasmon polariton modes to increase the surface sensitivities of silver capped nanoslits. The results indicate that the coupled resonance between the split SPR (&minus;kSPR) and cavity modes (two-mode coupling) has a high wavelength sensitivity for small-angle incidence (2&deg;) due to its short decay length. Additionally, three-mode coupling between the split SPR (&minus;kSPR), substrate (+kSub) and cavity modes has a high intensity sensitivity for large-angle incidence due to its short decay length, large resonance slope and enhanced transmission intensity. Compared to the wavelength measurement, the intensity measurement has a lower detectable (surface) concentration below 1&thinsp;ng/ml (0.14&thinsp;pg/mm2) and is reduced by at least 3 orders of magnitude. In addition, based on the calibration curve and current system noise, a theoretical detection limit of 2.73&thinsp;pg/ml (0.38&thinsp;fg/mm2) can be achieved. Such a surface concentration is close to that of prism-based SPR with phase measurement (0.1&ndash;0.2&thinsp;fg/mm2 under a phase shift of 5 mdeg).

f3: Refractive index sensing capabilities of the silver capped nanoslits with oblique-angle incidence.(a) A measured transmission diagram of the 520-nm-period silver capped nanoslits in different refractive index mixtures for different incident angles from 0° to 35°. (b) The measured transmission spectra in air for different incident angles from 0° to 20°. The measured transmission spectra in different refractive index mixtures for incident angles of (c), 0° and (d), 10°. The insets show the resonance wavelength against the refractive index for incident angles of 0° to 10°. (e) The bulk sensitivity versus the incident angle for different incident angles from 0° to 20°. (f ) The normalized decay lengths for a flat sliver surface and the capped nanoslits. The normalized decay lengths for the flat sliver surface were calculated using equation (3). The decay lengths for the capped nanoslits were calculated using equation (4). The measured bulk sensitivities and wavelength shifts caused by the adsorbate of BSA in Fig. 2i and the parameters d = 2.4 nm, na = 1.57 and ns = 1 were utilized.

Mentions:
The spectral shift is dominated by the bulk sensitivity (Sλ) and decay length (ld), as indicated in equation (4). To calculate the decay length, we first measured the bulk sensitivity by covering the capped nanoslit array with different refractive index media. Figure 3a shows the measured transmission diagram from 0° to 35°. Figure 3b shows the measured transmission spectra in air for different incident angles from 0° to 20°. As θ increases, the resonance peak splits into two resonances. Figure 3c,d show the measured transmission spectra in different refractive index mixtures for incident angles of 0° and 10°, respectively. The resonances were redshifted as the refractive index of the environment increased. There were linear correlations between the resonance wavelength and the refractive index of the environment for incident angles of 0° and 10° (see Fig. 3c inset and 3d inset). Figure 3e shows the bulk sensitivity versus the incident angle for different incident angles from 0° to 20°. The results show that when the incident angle changed from 0° to 20°, the bulk sensitivity decreased and increased within 10% for the forward- and backward-propagating coupled modes, respectively. According to equation (4), the decay lengths for different incident angles can be calculated with the measured bulk sensitivities, wavelength shifts and thicknesses of the biomolecules. Using the parameters d = 2.4 nm, na = 1.57 and ns = 1, the normalized decay lengths of the capped nanoslits for different incident angles are shown in Fig. 3f. Compared to the normal incidence, the decay length first substantially decreased and then gradually increased as θ increased. Compared to the theoretical decay length for SPR on a flat sliver surface, the Fano resonance in the capped nanoslit had a much shorter decay length (see Fig. 3f). The decay lengths reduced by factors of 2.5 and 1.5 for incident angles of 2° and 20°, respectively.

f3: Refractive index sensing capabilities of the silver capped nanoslits with oblique-angle incidence.(a) A measured transmission diagram of the 520-nm-period silver capped nanoslits in different refractive index mixtures for different incident angles from 0° to 35°. (b) The measured transmission spectra in air for different incident angles from 0° to 20°. The measured transmission spectra in different refractive index mixtures for incident angles of (c), 0° and (d), 10°. The insets show the resonance wavelength against the refractive index for incident angles of 0° to 10°. (e) The bulk sensitivity versus the incident angle for different incident angles from 0° to 20°. (f ) The normalized decay lengths for a flat sliver surface and the capped nanoslits. The normalized decay lengths for the flat sliver surface were calculated using equation (3). The decay lengths for the capped nanoslits were calculated using equation (4). The measured bulk sensitivities and wavelength shifts caused by the adsorbate of BSA in Fig. 2i and the parameters d = 2.4 nm, na = 1.57 and ns = 1 were utilized.

Mentions:
The spectral shift is dominated by the bulk sensitivity (Sλ) and decay length (ld), as indicated in equation (4). To calculate the decay length, we first measured the bulk sensitivity by covering the capped nanoslit array with different refractive index media. Figure 3a shows the measured transmission diagram from 0° to 35°. Figure 3b shows the measured transmission spectra in air for different incident angles from 0° to 20°. As θ increases, the resonance peak splits into two resonances. Figure 3c,d show the measured transmission spectra in different refractive index mixtures for incident angles of 0° and 10°, respectively. The resonances were redshifted as the refractive index of the environment increased. There were linear correlations between the resonance wavelength and the refractive index of the environment for incident angles of 0° and 10° (see Fig. 3c inset and 3d inset). Figure 3e shows the bulk sensitivity versus the incident angle for different incident angles from 0° to 20°. The results show that when the incident angle changed from 0° to 20°, the bulk sensitivity decreased and increased within 10% for the forward- and backward-propagating coupled modes, respectively. According to equation (4), the decay lengths for different incident angles can be calculated with the measured bulk sensitivities, wavelength shifts and thicknesses of the biomolecules. Using the parameters d = 2.4 nm, na = 1.57 and ns = 1, the normalized decay lengths of the capped nanoslits for different incident angles are shown in Fig. 3f. Compared to the normal incidence, the decay length first substantially decreased and then gradually increased as θ increased. Compared to the theoretical decay length for SPR on a flat sliver surface, the Fano resonance in the capped nanoslit had a much shorter decay length (see Fig. 3f). The decay lengths reduced by factors of 2.5 and 1.5 for incident angles of 2° and 20°, respectively.

Surface sensitivity is an important factor that determines the minimum amount of biomolecules detected by surface plasmon resonance (SPR) sensors. We propose the use of oblique-angle-induced Fano resonances caused by two-mode coupling or three-mode coupling between the localized SPR mode and long-range surface plasmon polariton modes to increase the surface sensitivities of silver capped nanoslits. The results indicate that the coupled resonance between the split SPR (&minus;kSPR) and cavity modes (two-mode coupling) has a high wavelength sensitivity for small-angle incidence (2&deg;) due to its short decay length. Additionally, three-mode coupling between the split SPR (&minus;kSPR), substrate (+kSub) and cavity modes has a high intensity sensitivity for large-angle incidence due to its short decay length, large resonance slope and enhanced transmission intensity. Compared to the wavelength measurement, the intensity measurement has a lower detectable (surface) concentration below 1&thinsp;ng/ml (0.14&thinsp;pg/mm2) and is reduced by at least 3 orders of magnitude. In addition, based on the calibration curve and current system noise, a theoretical detection limit of 2.73&thinsp;pg/ml (0.38&thinsp;fg/mm2) can be achieved. Such a surface concentration is close to that of prism-based SPR with phase measurement (0.1&ndash;0.2&thinsp;fg/mm2 under a phase shift of 5 mdeg).